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A250431 Number of (n+1)X(7+1) 0..1 arrays with nondecreasing sum of every two consecutive values in every row and column 1

%I

%S 625,5625,50625,275625,1500625,6002500,24010000,77792400,252047376,

%T 700131600,1944810000,4802490000,11859210000,26683222500,60037250625,

%U 125262905625,261351000625,512247961225,1004006004001,1866953313225

%N Number of (n+1)X(7+1) 0..1 arrays with nondecreasing sum of every two consecutive values in every row and column

%C Column 7 of A250432.

%H R. H. Hardin, <a href="/A250431/b250431.txt">Table of n, a(n) for n = 1..210</a>

%F Empirical: a(n) = 2*a(n-1) +14*a(n-2) -30*a(n-3) -90*a(n-4) +210*a(n-5) +350*a(n-6) -910*a(n-7) -910*a(n-8) +2730*a(n-9) +1638*a(n-10) -6006*a(n-11) -2002*a(n-12) +10010*a(n-13) +1430*a(n-14) -12870*a(n-15) +12870*a(n-17) -1430*a(n-18) -10010*a(n-19) +2002*a(n-20) +6006*a(n-21) -1638*a(n-22) -2730*a(n-23) +910*a(n-24) +910*a(n-25) -350*a(n-26) -210*a(n-27) +90*a(n-28) +30*a(n-29) -14*a(n-30) -2*a(n-31) +a(n-32)

%F Empirical for n mod 2 = 0: a(n) = (1/21743271936)*n^16 + (1/226492416)*n^15 + (89/452984832)*n^14 + (203/37748736)*n^13 + (2549/25165824)*n^12 + (1459/1048576)*n^11 + (1224205/84934656)*n^10 + (812447/7077888)*n^9 + (20096035/28311552)*n^8 + (2015611/589824)*n^7 + (3762023/294912)*n^6 + (149513/4096)*n^5 + (26016553/331776)*n^4 + (422071/3456)*n^3 + (12469/96)*n^2 + (505/6)*n + 25

%F Empirical for n mod 2 = 1: a(n) = (1/21743271936)*n^16 + (1/226492416)*n^15 + (535/2717908992)*n^14 + (1225/226492416)*n^13 + (185693/1811939328)*n^12 + (35725/25165824)*n^11 + (40404433/2717908992)*n^10 + (27184205/226492416)*n^9 + (8206068803/10871635968)*n^8 + (840056675/226492416)*n^7 + (476102705/33554432)*n^6 + (1052064899/25165824)*n^5 + (6239471239/67108864)*n^4 + (1265493285/8388608)*n^3 + (5650169175/33554432)*n^2 + (968932125/8388608)*n + (9845600625/268435456).

%F a(n+1) = A202098(n). - _R. J. Mathar_, Dec 02 2014

%e Some solutions for n=3

%e ..0..0..0..0..0..0..1..1....1..0..1..0..1..0..1..1....0..0..0..0..1..0..1..0

%e ..0..1..1..1..1..1..1..1....0..0..1..0..1..0..1..1....1..0..1..0..1..1..1..1

%e ..1..0..1..0..1..1..1..1....1..0..1..0..1..1..1..1....0..0..0..0..1..1..1..1

%e ..1..1..1..1..1..1..1..1....1..0..1..1..1..1..1..1....1..1..1..1..1..1..1..1

%K nonn

%O 1,1

%A _R. H. Hardin_, Nov 22 2014

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Last modified September 22 22:13 EDT 2021. Contains 347608 sequences. (Running on oeis4.)